Reduced order models for the prediction of the time of occurrence of extreme episodes

We describe in this paper a very special class of complex systems, namely t hose which admit reduced order models for the prediction of the peaks of a relevant variable (the output variable of the system). In particular, we sh ow that if the attractor of the system is a torus or a low-dimensional stra nge attractor, such reduced order models exist and allow one to forecast th e time of occurrence of the next peak, given the times of occurrence of the last three peaks. This property is particularly useful for forecasting rec urrent extreme episodes in ecosystems. (C) 2000 Elsevier Science Ltd. All r ights reserved.